Long-dated Calls

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I’m interested in the boards thoughts on the attractiveness of Deep in the money, long-dated Calls. Most of my Berkshire holdings are straight stock, but I have some $180 Calls that expire January 2024.
I’m holding about as much in these calls as I have in cash, so it balances out to keep me fully invested in Berkshire, but also holding some cash just in case. I recently sold a few covered calls for $460 because I think that’s crazy high and I would want to funds some cash at that level anyway - sort of a rebalancing plan.

Why the $180 calls are valuable:
Borrowing costs are still rather low, something like 3% per year on the borrowed strike price. You’d pay a total $360.85 for stocks selling at $349.66, but you’re putting up only $180.85, and borrowing $180.

It’s a better inflation hedge than the stock. If we see high inflation, and Berkshire’s stock price merely rises alongside it, a strategy that borrows on margin should outperform one that owns the stock.

They are the longest Berkshire LEAPS available.

Why I’m concerned:
The stock price has risen to where it’s not obviously clear that Berkshire will continue to outperform.

Despite the benefits, I’m considering selling the $180 calls to buy straight stock and solidify the gains we’ve seen this year, maybe leaving only enough $180 calls to balance out the $460 calls I’m short on. Is there anything else I should be looking at?

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I’m considering selling the $180 calls to buy straight stock

You may want to exercise your calls. Don’t sell and buy stock, the gains are taxable. Separately, still not clear to me why you want to own shares instead of calls.

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It’s hard to say what fits any given person’s situation.

But for me, a long time fan of deep long calls, the two things that make sense in a good valuation stretch like this are below.
You may not of thought much about option 2.

(1) I lighten up a bit. Entirely a matter of taste.

Sell a little, maybe write a few high-strike calls, turning long positions into covered calls.
The hope is to use that cash to buy something with higher prospective returns some time soon.
Maybe Berkshire, maybe something else.

For lightening, for example, I’ve written a few January $350 calls for a premium of $28.34.
Either I get to keep the $28.34 as “bonus” cash (about 9.7%/yr rate of “dividend” on the stock involved),
or I end up selling some stock at a “net” exit price of 378.34 per B = $567510 per share = 1.67 times current known book.
A person who has to sell a bit from time to time should not feel bad selling at that valuation level,
even though a share will surely be worth a little more by next January.

What’s the prospect of the price soaring a lot further this year?
Berkshire B-shares are trading at $352.80 in pre-market at the moment.
My sundry models observe that this sort of valuation level is consistent with one-year forward performance around inflation - 3.4%.
Range of the models inflation-10% to inflation+4.1%.
If you consider only the modern era of lower valuations since 2008, this sort of valuation level was typically followed by a one year return of about inflation - 7.9%.
The future will be different, but it gives a starting idea of short term outcomes that would not be surprising.
In short, it’s pretty likely we’ll see lower prices in future. No idea how much lower or when, but it seems pretty likely.

(2) I roll my calls up: sell your low-strike ones and buy the same number of higher-strike ones.
Or roll them up and out. (same thing, but both higher strike and later date).
As the stock price today is very much higher than it was, the time premium at any given strike price is very much lower than it was.
For example, a while back a $270 call would have been very aggressive and very expensive in time value, with a bad high breakeven price.
At today’s prices, that’s no longer nearly as true as it was. It would count as almost a reasonable choice now.

That doesn’t make it much less “risky” in the sense of the possibility of expiring worthless.
The value of a share hasn’t risen nearly as much as the price has in the last several months.
You always want to make sure you have the wherewithal to exercise calls, or sufficient cash to replace them with something new.

But rolling “up” it has a few advantages:

  • You keep the size of your long term position and are not relying on the iffy notion of being able to buy back at a cheaper price later.
    Nobody really knows how much the price will dip in future, nor when it might happen.
    Buying back at a lower price later is probably going to be possible, but hard to count on, and hard to pick your moment.

  • If the stock price plummets for a while, there is a very good chance you can do a nice trade:
    On a day that things are panicky and the price is low, sell your high strike calls.
    Roll them back down again to very low strikes or simply buy the corresponding amount of stock if you have the cash.
    This is nice because the effect above is reversed: in such a situation the time value of your high-strike puts really soars as the stock price comes down towards their strikes.
    You can lock in a pretty substantial amount of profit this way, again without reducing the size of your long term position.
    Phrased another way, you lose a lot less in current market value during a plunge when holding high-strike calls than you do holding low-strike calls.
    It’s like the air under a falling elevator car: the farther you fall, the more slowly you fall, gradually approaching the strike (the bottom of the shaft).
    And that extra cushion of time value can be sold and locked in.

  • Rolling “up” frees up a lot of cash, even though it hurts your breakeven a bit.
    That cash can have a lot of uses. Keep it for a rainy day, invest in something else, wait for a good investment deal, or even spend it.
    You can go for decades this way, pulling money out of your portfolio, while always having the upside on the same number of shares of Berkshire.
    More than any other thing, this is in effect how I make a living.

Jim

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Big question Jim.
With these options traded over the years, are your returns better than UF you had just held BRK all those years and sold as needed when valuation was reasonable. I.e. Dell to raise cash to last day a couple of years at a time when valuation appears reasonable.

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Sorry.
UF is if
Dell is sell

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Big question Jim.
With these options traded over the years, are your returns better than UF you had just held BRK all
those years and sold as needed when valuation was reasonable. I.e. Dell to raise cash to last day a
couple of years at a time when valuation appears reasonable.

The “buy and hold” return on Berkshire has been 10.52%/year since I bought my first share.
My “excess” returns beyond that level come from a lot of sources.
Buying low, selling high, adding fresh capital from other sources at good times, and leverage from calls.
Some very fancy option trades. Covered calls, single stock futures.
Minus some unfortunate moves like pulling money out at inopportune moments because of other things going on in my life.

But alas, by far the biggest gain beyond the “buy and hold” return is attributable simply to the cheap leverage that calls have provided so far. I’m a bad person.
And the fact that I started that leverage in a big way during a stretch of very attractive valuations around 2011-2012.
It was pretty scary at first, but I built up speed.

Buying low and selling high definitely works, but not as well as you might think.
The reason is that, though selling on strength is pretty easy, buying on dips is really really hard.
You never know how cheap things are going to get, so you tend to jump back in after only a small dip, fearing it won’t go lower and “get away from you”.
So you make a nice profit selling high and buying low, but not nearly as much as the charts would suggest.
I think I did a fine job selling into strength in late 2007. Various P/B from 1.706 to 1.904. Nice move.
But the profit was small…I got back in much too soon, with hindsight.
I think I was back up to the same share count by January 2008, long before the big price plunge.
Because nobody knew in advance that entry points that good would be available.

My overall IRR (return on dollar-days of capital at risk) in Berkshire since inception is kind of crazy.
20.54 years at 29.05%/year compounded after all fees and leverage costs.
I have done 3245 trades.
If I hadn’t spent all the profits along the way, I’d be pretty rich.
But I have had a lot of fun with the profits, so that’s better.

Jim

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Jim, if taxes on these incredible gains were a consideration , would you have taken a completely different approach?
1.2905 to the 20.54 is one really big return, 188:1 !!!
For us USA mortals, it seems April 15th is always a big part of our investment decision and your returns would also get into our maximum estate exclusion & 40% tax rates.

ciao

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Jim, if taxes on these incredible gains were a consideration , would you have taken a completely different approach?

Sure, it would be different. Tax matters. A lot of the trades I did were essentially “frictionless”.
But tax doesn’t matter nearly as much as most people worry about it.
It seems a lot of people let the tail wag the dog, especially those in the situation that they’re merely deferring it, not avoiding it.
For them, the benefit is not the value of the tax, but “merely” the time value of the tax, a very different number.

But I’d still be using calls, and paying the tax every two years, since the benefit is so large.
This is true only so long as the real implied interest rates remain attractive, then the party will end.
And Berkshire’s valuation level has be be attractive relative to expected business results.

1.2905 to the 20.54 is one really big return, 188:1 !!!

Yeah.
But you can’t turn that IRR into a real CAGR annual rate with no withdrawals, as a lot of the
returns occurred only in short stretches of strong price rises while I was heavily invested.
It only worked as a high rate of return on days of capital at risk because I wasn’t fully long all the time.
A lot of times I’d tick along with a modest position, wait for a good entry, then pounce with gusto for a while.
Not right now, I might add.

Jim

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Jim, I so appreciate your open candid postings of your personal experiences and for me, more importantly, the continued education I am receiving from your reasoning!
My original post probably expresses it best……

https://discussion.fool.com/best-grad-school-in-the-ether-331429…

ciao

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The “buy and hold” return on Berkshire has been 10.52%/year since I bought my first share.

I just had a look: 11.3% CAGR since in 2000 I bought my first shares which are also the majority of my Berkshire holdings. But the very best:

! ANNIVERSARY !

They are nearly exactly 10x worth what I paid for them in 2000!

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Yeah.
But you can’t turn that IRR into a real CAGR annual rate with no withdrawals, as a lot of the
returns occurred only in short stretches of strong price rises while I was heavily invested.
It only worked as a high rate of return on days of capital at risk because I wasn’t fully long all the time.
A lot of times I’d tick along with a modest position, wait for a good entry, then pounce with gusto for a while.
Not right now, I might add.

Does that mean your 29% IRR was not averaged over the whole time? That, for example, if had been doing this in an account worth $1,000,000 that you would not have been able to extract about $290,000 per year (on average)? Is this typical of an IRR? I have been assuming without doing any testing that “random” withdrawals would not change the IRR. Maybe I should check this.

R:

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Does that mean your 29% IRR was not averaged over the whole time?

Correct.
It was average over the whole time, as I have always had some Berkshire positions…
but any given stretch is weighted only in proportion to my position size at the time.

For every day, I calculate how many dollars of capital I have at risk (= what I’d lose that day if it went to zero forever).
Add those up for every day since I bought my first share, and I get the total dollar-days I’ve had at risk.
Divide by 365, and that’s the total number of dollar-years of capital at risk.

Divide my total profit to date by the number of dollar-years of capital committed above, and that’s the internal rate of return (IRR).
But there will be some times of falling stock price that I was (largely) out of the stock, so it’s not the same as a CAGR–I wasn’t long the same amount all the time.

That, for example, if had been doing this in an account worth $1,000,000 that you would not have been able to extract about $290,000 per year (on average)?

If I had had an account averaging $1,000,000 at risk on any given day, then I could have (and did) pull out $290k per year on average.
But the amount of money at risk on a given day would probably have varied quite a bit, maybe from $500k to $1.5m.
The key word is “average”.

In short, it really worked, but it only worked because I had other investments (including a cash reserve and a mortgage)
which I could move money to and from when I added to or lightened up on my Berkshire position based on its attractiveness.

FWIW, at the moment I have less than half the “money at risk” exposure to Berkshire that I have averaged in recent years.
Not just because of valuation levels. I have other things going on in my life which produce or consume money.

Jim

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Jim wrote:
If I had had an account averaging $1,000,000 at risk on any given day, then I could have (and did) pull out $290k per year on average.
But the amount of money at risk on a given day would probably have varied quite a bit, maybe from $500k to $1.5m.
The key word is “average”.

In short, it really worked, but it only worked because I had other investments (including a cash reserve and a mortgage)
which I could move money to and from when I added to or lightened up on my Berkshire position based on its attractiveness.

How many times have I said I learn something from Jim? Well today I learned I didn’t really know what IRR was.

My takeaways at this point, and please correct me where I am getting this wrong, are as follows.

IRR depends on the actual cash flows in and out of the account! So IRR is a metric of how good an investment is, but the “investment” it measures includes the effect of actual withdrawals and deposits. So if withdrawals and deposits are being made strategically, IRR gives a metric which is a combination of the investment itself (e.g., BRK stock and options) and the strategy for investing and disinvesting over the life of the investment. It was be as if you were in a mutual or hedge fund which would dictate when it would send you cash from your investment, and when it would demand cash from you to put in your investment, then IRR would be the proper way to calculate how well that Hedge fund was treating you. Except it wouldn’t allow you to evalue the “cost” to you of having to take cash when they wanted and having to produce cash when they wanted.

The 29% number I have been calling IRR for Saul for 1988 thru 2021 inclusive, it turns out, is an IRR. But it is the IRR where the SAUL stocks are invested in in 1988, all the money is left 100% in stock but rebalanced as Saul determines, and then removed at the end of end of 2021. So there is a cash flow in of $1 in 1988 and a cash flow out of $4,486.88 in 2021, and that is an IRR of 29%.

Since it apparently matters, I tried two other cash flow strategies, but with the same annual returns reported for Saul, to see how they might change things.

First, I figured I’ll just take the earnings (or refund the losses) every year. So my cash flows are,

  1. $1 to get into the stocks in 1988,

  2. an average of $0.36 a year earnings but lumpy, ranging from $2.33 one year to -$0.63 paid back in a different year.

  3. Taking out my $1 principal plus my final earned interest in 2021.

In this case, my IRR is 27%, not that much different from 29%.

Second, I tried just taking a steady 25% of my previous years balance each year. This pulls my IRR down to 26% and also gives me a decade of about $0.06 a year to live on in the 2010-2020 range.

Third, I tried a few other interest rates and they tend to leave IRR in the 25+% range.

So for the SAUL annual returns, 1989-2021, it seems hard-ish to get IRR much lower than 25%, but of course I didn’t try any extreme tricks. So even though 25% IRR getting paid 20% of the balance per year to live on is not quite 29%, it is sustainable on the minimal testing I’ve done. No doubt you would either want to take a lot less or do some serious testing of hypothetical future returns before being that aggressive.

By the way, I am using Excel’s function to calculate IRR, not the average capital-years at risk dividing the total profits. I assume your intuitively interesting formulation and Excels are in agreement?

So regarding your own performance with BRK and long BRK calls and covered short BRK calls…

Presumably your “in” and your “out” are sufficiently different in magnitude and duration that you would need something like a peak of $10million in your strategy to average something like $1million in your strategy, which is to say in order to get $290,000 per year you would have to be deciding, most of the time, what to do with the other $9,000,000?

When you write covered calls, you presumably are booking the owned underlying shares as capital invested. So if you are really swinging a lot, you are spending a significant amount of time where you are both low on BRK stock and not writing covered calls. How do you determine when NOT to harvest time value from covered calls even though you don’t think the stock is going up? I presume a period of stock+CoveredCalls is not quite as short as being out of both, and that is how you decide?

So some low Price/Book has you long calls (and stock?),

some higher but still low P/B has you long stock but not calls,

some middling P/B has you in stock but with covered calls

some higher P/B has you out of stock and calls holding cash waiting for P/B to drop to get back in?

Anyway, I am very happy to understand IRR significantly better than I did. Thanks for that and for the insights on the moving pieces of stock and covered calls.

My own trading is in tax deferred us retirement accounts, so I don’t worry about tax per se, but I am limited to long calls long puts and covered calls and unable to write naked calls or naked puts.

Cheers,
R:)

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@RaplhCramden and @mungofitch,

I followed your back and forth discussion on IRR with great interest. I do have a basic comment regarding the use of IRR and CAGR and would like to know what you both think. It seems to me that sometimes the use of IRR can give misleading returns one cannot really enjoy as much as the numbers imply.

Let us think of the following (made-up) two examples:

In the first case, an investment of $1 was made on day 1, sold for $1.20 at the end of year 1, did nothing for 8 following years, and then at the beginning of year 10, invest again the same $1 and and sell it for $1.20 at the end of the tenth year. Now the IRR over the 10 year period is 20% and the investor took out a total profit of $0.40 (let us assume capital gains taxes are zero).

Now let us consider the second example where the investor buys the same investment on day 1 for $1 and sells it after 10 years for $2.84, thus getting a total profit of $1.84 over the 10 year period even though his CAGR (and also his IRR) is lower at 11%, far less than the IRR of 20% in the previous example.

Thus it seems to me that it is better to own an investment with a decent (but) lower CAGR and let it compound for a very very long time (as in Berkshire stock) than achieve a higher IRR by getting in and out of such investment. The total profit achieved would be way higher as shown in the example. For US based tax payers, the advantage of what Munger calls “sit-on-your-ass” investment style is even more one-sided.

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In the first case, an investment of $1 was made on day 1, sold for $1.20 at the end of year 1, did
nothing for 8 following years, and then at the beginning of year 10, invest again the same $1 and and
sell it for $1.20 at the end of the tenth year. Now the IRR over the 10 year period is 20% and the
investor took out a total profit of $0.40 (let us assume capital gains taxes are zero).

That’s indeed how it works.
In extreme situations like that, they can be very misleading.

In my case, the variation in capital at risk hasn’t been that large.
It has been mostly at its average level, plus or minus 40-45%. (using the 20th and 80th percentile of capital at risk over time).

It is possible to convert an IRR into a CAGR, in a conservative way:
Given the list of capital “ins” and “outs”, you can calculate the smallest pile of funds you would have had to have started with if you had made no deposits or withdrawals after starting.
Think of it as a portfolio which held nothing but the investment in question and zero-return cash at any time, moving only between the two, never adding anything.
The total profits, time interval, and that minimum starting number can give you a CAGR.

In my case that would be a CAGR of only 9.8%/year.
But that is much lower not so much because of the difference in calculation between IRR and CAGR, but more because there wasn’t any compounding.
I don’t own any more shares now than I did at the beginning, so that CAGR is based on a portfolio that had a higher
and higher percentage of cash stacking up from liquidated profits along the way, and ends today at 93% cash.
(my capital at risk today is 7% of the sum of minimum required starting capital to do all the trades plus profits to date)
The trades were sized based on pumping money out of the portfolio on regular basis, not resized based on the compounding goal that this calculation implicitly assumes.

Jim

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I have used MIRR to calculate the return for a variable gain/loss income stream.
The attached link gives examples & an explanation of the differences between IRR & MIRR.

https://corporatefinanceinstitute.com/resources/excel/study/…

ciao

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Thanks @mungofitch for the detailed response.

It is possible to convert an IRR into a CAGR, in a conservative way

Just to clarify your method of approximately converting IRR to CAGR, if I apply it to my example 1, the minimum starting capital would be $1 and CAGR over 10-year time period would be 3.4%. Please let me know if this is correct.

In my case that would be a CAGR of only 9.8%/year.
But that is much lower not so much because of the difference in calculation between IRR and CAGR, but more because there wasn’t any compounding.

I think you hit the nail on the head. The main disadvantage of IRR is that it doesn’t provide an accurate picture of compounded results unlike CAGR which does.

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I think you hit the nail on the head. The main disadvantage of IRR is that it doesn’t provide an accurate picture of compounded results unlike CAGR which does.

Makes sense.

They’re both right. They just mean different things.

To me, the main question is whether you consider the decisions about when to invest and disinvest as as part of the
investment strategy whose performance you’re trying to characterize, or as independent events decided by some third party in an unrelated way.

Imagine a guy who buys and sells houses for a living.
He has a lot of big lumps of capital coming in and going out from time to time.
Each time he gets a lump of money from a sale, he plunks it into Mr Bean’s Hedge Fund.
Each time he buys a new place, he withdraws it from the fund.

In this case, the investment “in and out” decisions are entirely divorced from the underlying investment. Mr Bean had nothing to say about them.
An IRR makes a lot of sense as a way to get a handle on how the Bean Fund did for the real estate guy.
How well did he do, on average, with the dollars he had invested while they were invested?

But for (say) many private equity funds, the investment manager is getting to say when to put the money in or when you get it back.
It is an inextricable part of the investment strategy, not something at the option of the investor,
so a CAGR is more appropriate: overall end to end return based on the capital tied up.
Cash which could be called upon at any time isn’t available for any other use, so in most practical senses it’s already in the fund.
Unsurprisingly, they prefer to do their marketing with IRR.

Another way I could estimate the rate of my returns:
Consider all my withdrawals as one would consider dividends.
It’s fairly reasonable to consider the long run return on any investment as the sum of two numbers:

  • The end-to-end CAGR of the portfolio, ignoring the fact that money was taken out.
    Ending balance divided by starting balance, raised to the power of the inverse of the number of years elapsed.
    …plus…
  • The average annual dividend yield: average across time of (money withdrawn in a given year) / (average capital in the portfolio during that year).
    This is in many ways a more realistic way to consider the returns on SPY than the usual unrealistic assumptions about dividend reinvestment.

Jim

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But for (say) many private equity funds, the investment manager is getting to say when to put the money in or when you get it back.
It is an inextricable part of the investment strategy, not something at the option of the investor,
so a CAGR is more appropriate: overall end to end return based on the capital tied up.
Cash which could be called upon at any time isn’t available for any other use, so in most practical senses it’s already in the fund.
Unsurprisingly, they prefer to do their marketing with IRR.

+1, agree 100%. PE is classic example of misuse of IRR. They quote IRR because it is self serving for the fund managers and they can attract dumb LPs who think they are getting CAGR.

Another way I could estimate the rate of my returns:
Consider all my withdrawals as one would consider dividends.
It’s fairly reasonable to consider the long run return on any investment as the sum of two numbers:
* The end-to-end CAGR of the portfolio, ignoring the fact that money was taken out.
Ending balance divided by starting balance, raised to the power of the inverse of the number of years elapsed.
…plus…
* The average annual dividend yield: average across time of (money withdrawn in a given year) / (average capital in the portfolio during that year).
This is in many ways a more realistic way to consider the returns on SPY than the usual unrealistic assumptions about dividend reinvestment.

If I use this method in my example 1, I get 4.0% CAGR instead of 3.4% using your previous method. But they are both in the same ballpark. I do agree that this is a decent way of estimating the CAGR with multiple distributions.

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@mungofitch wrote:

For every day, I calculate how many dollars of capital I have at risk (= what I’d lose that day if it went to zero forever).
Add those up for every day since I bought my first share, and I get the total dollar-days I’ve had at risk.
Divide by 365, and that’s the total number of dollar-years of capital at risk.

Divide my total profit to date by the number of dollar-years of capital committed above, and that’s the internal rate of return (IRR).
But there will be some times of falling stock price that I was (largely) out of the stock, so it’s not the same as a CAGR–I wasn’t long the same amount all the time.

I believe this approximation (as I understand it) works well only when there are lots of trades (of somewhat short period in between them) in and out of the portfolio. It fails when the holding period between the “in” and “out” is long.

As an example, if I buy an investment on day 1 for $1 and hold it for 10 years and sell it for $2 at the end of 10 years, then this calculation gives an IRR of 10% (100%/10) when the actual IRR is 7%. In general I think the approximate calculation overstates the actual IRR.

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